Predictive models used to estimate the resilient modulus of subgrade soil for pavement design
DOI:
https://doi.org/10.58922/transportes.v34.e3209Keywords:
Artificial intelligence; Resilient modulus; Pavement design; Soil prediction; Low volume roads.Abstract
Obtaining the resilient modulus (MR) of the subgrade soils to be used in mechanistic empirical pavement design models, such as MeDiNa, is a complex and expensive process, due to the high costs of acquiring and operating the repeated triaxial load testing equipment. This study investigated the use of Artificial Neural Networks (ANN) to create models for the prediction of the MR of soils based on their index properties. A database was created for the modeling with experimental datasets obtained from the state of Ceará, Brazil. The results indicated that the ANN is able to predict the MR of the subgrade soil very accurately (with a correlation of 0.9878 for the test dataset). These results were used to generate estimates that can be included in an integrated approach to the mechanistic-empirical pavement design in Brazil (MeDiNa), which reduces both the financial costs and the execution time of projects, especially for the design of low-volume roads.
Downloads
References
AASHTO (2008). Mechanistic-Empirical Pavement Design Guide: AManual of Practice. Washington, D.C.: American Association of State Highway and Transportation Officials. URL: https://trid.trb.org/View/884665 [visited 18/6/2026].
ABNT (1984). NBR 7181: Análise Granulométrica de Solos. Rio de Janeiro: Associação Brasileira de Normas Técnicas. ABNT (2016a). NBR 6459: Determinação do Limite de Liquidez dos Solos. Rio de Janeiro: Associação Brasileira de Normas Técnicas.
ABNT (2016b). NBR 7180: Determinação do Limite de Plasticidade de Solos. Rio de Janeiro: Associação Brasileira de Normas Técnicas.
ABNT (2016c). NBR 9895: Método de Ensaio do California Bearing Ratio (CBR). Rio de Janeiro: Associação Brasileira de Normas Técnicas.
ABNT (2019). NBR 7182: Ensaio de Compactação de Solos. Rio de Janeiro: Associação Brasileira de Normas Técnicas. Alawi, M. & M. Rajab (2013). Prediction of California bearing ratio of subbase layer using multiple linear regression models. Road Materials and Pavement Design 14(1), 211–219. DOI:10.1080/14680629.2012.757557. DOI: https://doi.org/10.1080/14680629.2012.757557
Baghbani, A., T. Choudhury, S. Costa, & J. Reiner (2022). Application of artificial intelligence in geotechnical engineering: a state-of-the-art review. Earth-Science Reviews 228, 103991. DOI:10.1016/j.earscirev.2022.103991. DOI: https://doi.org/10.1016/j.earscirev.2022.103991
Bastos, J. B. S. (2013). Influência da variação da umidade no comportamento de pavimentos da região metropolitana de fortaleza. Dissertação (mestrado) – engenharia de transportes, Universidade Federal do Ceará, Fortaleza, CE.
Beale, M. H., M. T. Hagan, & H. B. Demuth (2010). Neural Network Toolbox 7: Users Guide. Natick: The MathWorks.
Boruvka, L. & V. Penizek (2007). Test of an artificial neural network allocation procedure using the Czech soil survey of agricultural land data. In P. Lagacherie, A. B. McBratney, & M. Voltz (Eds.), Digital Soil Mapping: an Introductory Perspective, pp. 415–424. Amsterdam: Elsevier. DOI: https://doi.org/10.1016/S0166-2481(06)31030-6
Bounds, D. G., P. J. Lloyd, B. Mathew, & G. Waddell (1988). A multilayer perceptron network for the diagnosis of low back pain. In Proceedings of the 2nd IEEE International Conference on Neural Networks, New York, pp. 481–489. IEEE. DOI: 10.1109/ICNN.1988.23963. DOI: https://doi.org/10.1109/ICNN.1988.23963
Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals, and Systems 2(4), 303–314. DOI:10.1007/BF02551274. DOI: https://doi.org/10.1007/BF02551274
Dai, S. & J. Zollars (2002). Resilient modulus of Minnesota road research project subgrade soil. Transportation Research Record: Journal of the Transportation Research Board 1786(1), 20–28. DOI:10.3141/1786-03. DOI: https://doi.org/10.3141/1786-03
Dhar, S. & M. Hussain (2021). The strength and microstructural behavior of lime stabilized subgrade soil in road construction. International Journal of Geotechnical Engineering 15(4), 471–483. DOI:10.1080/19386362.2019.1598623. DOI: https://doi.org/10.1080/19386362.2019.1598623
DNIT (2010). Determinação do Módulo de Resiliência de Solos: Método de Ensaio. Rio de Janeiro: Departamento Nacional de Infraestrutura de Transportes.
DNIT (2018). DNIT 134/2018 - ME: Pavimentação – Solos – Determinação do Módulo de Resiliência – Método de Ensaio. Rio de Janeiro: Instituto de Pesquisas Rodoviárias (IPR).
Erzin, Y. & D. Turkoz (2016). Use of neural networks for the prediction of the CBR value of some Aegean sands. Neural Computing & Applications 27(5), 1415–1426. DOI:10.1007/s00521-015-1943-7. DOI: https://doi.org/10.1007/s00521-015-1943-7
Esmaeili, M., A. Khodaverdian, H. K. Neyestanaki, & S. Nazari (2016). Investigating the effect of nailed sleepers on increasing the lateral resistance of ballasted track. Computers and Geotechnics 71, 1–11. DOI:10.1016/j.compgeo.2015.08.006. DOI: https://doi.org/10.1016/j.compgeo.2015.08.006
Ghanizadeh, A. R. & A. Delaram (2021). Development of predicting model for clay subgrade soil resilient modulus based on the results of cone penetration test using evolutionary polynomial regression method. Civil Infrastructure Researches 7(1), 93–109. DOI:10.22091/cer.2021.7122.1267.
Ghanizadeh, A. R. & N. Heidarabadizadeh (2024). Application of hybrid wavelet neural network and TLBO optimization algorithm for modeling the resilient modulus of granular subbase materials. Journal of Transpersonal Research 21(2), 127–150. DOI:10.22034/tri.2021.269667.2856.
Ghanizadeh, A. R., N. Heidarabadizadeh, & F. Heravi (2021). Gaussian process regression (GPR) for auto-estimation of resilient modulus of stabilized base materials. Journal of Soft Computing in Civil Engineering 5(1), 80–94. DOI:10.22115/scce.2021. 269187.1273.
Gunaydin, O., A. Gokoglu, & A. M. Fener (2010). Prediction of artificial soils unconfined compression strength test using statistical analyses and artificial neural networks. Advances in Engineering Software 41(9), 1115–1123. DOI:10.1016/j. advengsoft.2010.06.008. DOI: https://doi.org/10.1016/j.advengsoft.2010.06.008
Haykin, S. S. (2007). Neural Networks: a Comprehensive Foundation (2nd ed.). Upper Saddle River: Pearson. Hecht-Nielsen, R. (1989). Neurocomputing. Boston: Addison-Wesley.
Heidarabadizadeh, N., A. R. Ghanizadeh, & A. Behnood (2021). Prediction of the resilient modulus of non-cohesive subgrade soils and unbound subbase materials using a hybrid support vector machine method and colliding bodies optimization algorithm. Construction & Building Materials 275, 122140. DOI:10.1016/j.conbuildmat.2020.122140. DOI: https://doi.org/10.1016/j.conbuildmat.2020.122140
Johari, A., A. A. Javadi, & G. Habibagahi (2011). Modelling the mechanical behaviour of unsaturated soils using a genetic algorithm-based neural network. Computers and Geotechnics 38(1), 2–13. DOI:10.1016/j.compgeo.2010.08.011. DOI: https://doi.org/10.1016/j.compgeo.2010.08.011
Kayadelen, C., O. Gunaydin, M. Fener, A. Demir, & A. Özvan (2009). Modeling of the angle of shearing resistance of soils using soft computing systems. Expert Systems with Applications 36(9), 11814–11826. DOI:10.1016/j.eswa.2009.04.008. DOI: https://doi.org/10.1016/j.eswa.2009.04.008
Khasawneh, M. A. & N. F. Al-Jamal (2019). Modeling resilient modulus of fine-grained materials using different statistical techniques. Transportation Geotechnics 21, 100263. DOI:10.1016/j.trgeo.2019.100263. DOI: https://doi.org/10.1016/j.trgeo.2019.100263
Kim, D. & J. R. Kim (2007). Resilient behavior of compacted subgrade soils under the repeated triaxial test. Construction & Building Materials 21(7), 1470–1479. DOI:10.1016/j.conbuildmat.2006.07.006. DOI: https://doi.org/10.1016/j.conbuildmat.2006.07.006
Kim, S. H., J. Yang, & J. H. Jeong (2014). Prediction of subgrade resilient modulus using artificial neural networks. KSCE Journal of Civil Engineering 18(5), 1372–1379. DOI:10.1007/s12205-014-0316-6. DOI: https://doi.org/10.1007/s12205-014-0316-6
Lacerda, J. P., Y. V. Dias, F. S. Costa, N. Batista, & A. Ribeiro (2024). Design and validation of a regression model for soil resilience modulus applied in the empirical-mechanistic design of pavements. Revista Matéria 29(3), e20230220. DOI:10.1590/1517-7076-RMAT-2023-0220. DOI: https://doi.org/10.1590/1517-7076-rmat-2023-0220
Li, M. & H. Wang (2019). Development of ANN-GA program for backcalculation of pavement moduli under FWD testing with viscoelastic and nonlinear parameters. The International Journal of Pavement Engineering 20(4), 490–498. DOI: 10.1080/10298436.2017.1309197. DOI: https://doi.org/10.1080/10298436.2017.1309197
Liu, Y., D. Stolle, P. Guo, & J. Emery (2014). Stress-path dependency of resilient behaviour of granular materials. The International Journal of Pavement Engineering 15(7), 614–622. DOI:10.1080/10298436.2013.808340. DOI: https://doi.org/10.1080/10298436.2013.808340
Mollahasani, A., A. H. Alavi, A. H. Gandomi, & A. Rashed (2010). Nonlinear neural-based modeling of soil cohesion intercept. KSCE Journal of Civil Engineering 15(5), 831–840. DOI:10.1007/s12205-011-1154-4. DOI: https://doi.org/10.1007/s12205-011-1154-4
Mousavi, S. H., M. A. Gabr, & R. H. Borden (2018). Resilient modulus prediction of soft low-plasticity Piedmont residual soil using dynamic cone penetrometer. Journal of Rock Mechanics and Geotechnical Engineering 10(2), 323–332. DOI: 10.1016/j.jrmge.2017.10.007. DOI: https://doi.org/10.1016/j.jrmge.2017.10.007
Nazzal, M. D. & O. Tatari (2013). Evaluating the use of neural networks and genetic algorithms for prediction of subgrade resilient modulus. The International Journal of Pavement Engineering 14(4), 364–373. DOI:10.1080/10298436.2012.671944. NCHRP (2004). Guide for mechanistic-empirical design of new and rehabilitated pavement structures. Technical report, DOI: https://doi.org/10.1080/10298436.2012.671944
Transportation Research Board, National Research Council, Washington, D.C. URL: https://trid.trb.org/View/703699 [visited 18/6/2026].
Nguyen, B. T. & A. Mohajerani (2017). Possible estimation of resilient modulus of fine-grained soils using a dynamic lightweight cone penetrometer. The International Journal of Pavement Engineering 18(6), 473–484. DOI:10.1080/10298436.2015. 1095899. DOI: https://doi.org/10.1080/10298436.2015.1095899
Osouli, A., P. Adhikari, E. Tutumluer, & H. Shoup (2021). Properties of aggregate fines influencing modulus and deformation behaviour of unbound aggregates. The International Journal of Pavement Engineering 22(4), 498–513. DOI:10.1080/ 10298436.2019.1623402. DOI: https://doi.org/10.1080/10298436.2019.1623402
Pal, M. & S. Deswal (2014). Extreme learning machine based modeling of resilient modulus of subgrade soils. Geotechnical and Geological Engineering 32(2), 287–296. DOI:10.1007/s10706-013-9710-y. DOI: https://doi.org/10.1007/s10706-013-9710-y
Park, H. I., G. C. Kweon, & S. R. Lee (2009). Prediction of resilient modulus of granular subgrade soils and subbase materials using artificial neural network. Road Materials and Pavement Design 10(3), 647–665. DOI:10.1080/14680629.2009.9690218. DOI: https://doi.org/10.3166/rmpd.10.647-665
Patel, R. S. & M. D. Desai (2010). CBR predicted by index properties for alluvial soils of South Gujarat. In Indian Geotechnical Conference, GEOtrendz, IIT Bombay.
Pavini, M. (2002). Artificial neural network modeling of pavement performance using expert judgement. Road Materials and Pavement Design 3(4), 373–384. DOI:10.1080/14680629.2002.9689931. DOI: https://doi.org/10.1080/14680629.2002.9689931
Pezo, R. F. (1993). A general method of reporting resilient modulus tests of soils: a pavement engineer’s point of view. In 72nd Annual Meeting of the Transportation Research Board, Washington, D.C. National Academies.
Rahim, A. (2005). Subgrade soil index properties to estimate resilient modulus for pavement design. The International Journal of Pavement Engineering 6(3), 163–169. DOI:10.1080/10298430500140891. DOI: https://doi.org/10.1080/10298430500140891
Rahman, M. S. & S. Erlingsson (2015). A model for predicting permanent deformation of unbound granular materials. Road Materials and Pavement Design 16(3), 653–673. DOI:10.1080/14680629.2015.1026382. DOI: https://doi.org/10.1080/14680629.2015.1026382
Rakesh, N., A. K. Jain, A. M. Reddy, & K. SudhakarReddy (2006). Artificial neural networks-genetic algorithm based model for backcalculation of pavement layer moduli. The International Journal of Pavement Engineering 7(3), 221–230. DOI:10.1080/10298430500495113. DOI: https://doi.org/10.1080/10298430500495113
Ramos, A., A. G. Correia, B. Indraratna, T. Ngo, R. Calçada, & P. A. Costa (2020). Mechanistic-empirical permanent deformation models: Laboratory testing, modelling and ranking. Transportation Geotechnics 23, 100326. DOI:10.1016/j.trgeo.2020. 100326. DOI: https://doi.org/10.1016/j.trgeo.2020.100326
Ribeiro, A. J., C. A. Silva, & S. H. Barroso (2015). Neural estimation of localization and classification of soils for use in low-traffic-volume roads. Transportation Research Record: Journal of the Transportation Research Board 2473(1), 98–106. DOI:10.3141/2473-12. DOI: https://doi.org/10.3141/2473-12
Ribeiro, A. J., C. A. Silva, & S. H. Barroso (2018). Metodologia de baixo custo para mapeamento geotécnico aplicado à pavimentação. Transportes 26(2), 84–100. DOI:10.14295/transportes.v26i2.1491. DOI: https://doi.org/10.14295/transportes.v26i2.1491
Sadrossadat, E., H. Ali, & B. Ghorbani (2018). Towards application of linear genetic programming for indirect estimation of the resilient modulus of pavements subgrade soils. Road Materials and Pavement Design 19(1), 139–153. DOI:10.1080/ 14680629.2016.1250665. DOI: https://doi.org/10.1080/14680629.2016.1250665
Sadrossadat, E., H. Ali, & O. Saeedeh (2016). Prediction of the resilient modulus of flexible pavement subgrade soils using adaptive neuro-fuzzy inference systems. Construction & Building Materials 123, 235–247. DOI:10.1016/j.conbuildmat. 2016.07.008. DOI: https://doi.org/10.1016/j.conbuildmat.2016.07.008
Silva, L. V., T. V. Omido, C. S. Barboza, & A. R. Omido (2023). Dimensionamento de pavimentos flexíveis: análise comparativa de custos entre diferentes métodos. Revista Delos 16(46), 2474–2498. DOI:10.55905/rdelosv16.n46-030. DOI: https://doi.org/10.55905/rdelosv16.n46-030
Singh, M., A. Trivedi, & S. K. Shukla (2019). Strength enhancement of the subgrade soil of unpaved road with geosynthetic reinforcement layers. Transportation Geotechnics 19, 54–60. DOI:10.1016/j.trgeo.2019.01.007. DOI: https://doi.org/10.1016/j.trgeo.2019.01.007
Sitton, J. D., Y. Zeinali, & B. A. Story (2017). Rapid soil classification using artificial neural networks for use in constructing compressed earth blocks. Construction & Building Materials 138, 214–221. DOI:10.1016/j.conbuildmat.2017.02.006. DOI: https://doi.org/10.1016/j.conbuildmat.2017.02.006
Souza, W. M., A. J. Ribeiro, & C. A. Silva (2022). Use of artificial neural networks and visual-manual classification for prediction of soil properties for paving purposes. The International Journal of Pavement Engineering 23(5), 1482–1490. DOI:10.1080/10298436.2020.1807546. DOI: https://doi.org/10.1080/10298436.2020.1807546
Tanyildizi, M. & I. Gökalp (2025). Stabilization of expansive road subgrades with waste paper sludge: resilient modulus, artificial neural networks and modeling approach. Transportation Geotechnics 52, 101552. DOI:10.1016/j.trgeo.2025.101552. DOI: https://doi.org/10.1016/j.trgeo.2025.101552
Taskiran, T. (2010). Prediction of California bearing ratio of fine-grained soils by artificial intelligence methods. Advances in Engineering Software 41, 886–892. DOI:10.1016/j.advengsoft.2010.01.003. DOI: https://doi.org/10.1016/j.advengsoft.2010.01.003
Tenpe, A. R. & A. Patel (2018). Application of genetic expression programming and artificial neural network for prediction of California bearing ratio. Road Materials and Pavement Design 19, 1–18. DOI:10.1080/14680629.2018.1544924. DOI: https://doi.org/10.1080/14680629.2018.1544924
Yildirim, B. & O. Gunaydin (2011). Estimation of California bearing ratio by using soft computing systems. Expert Systems with Applications 38(5), 6381–6391. DOI:10.1016/j.eswa.2010.12.054. DOI: https://doi.org/10.1016/j.eswa.2010.12.054
Zaman, M., D. H. Chen, & J. Laguros (1994). Resilient modulus of granular materials. Journal of Transportation Engineer-ing 120(6), 967–988. DOI:10.1061/(ASCE)0733-947X(1994)120:6(967). DOI: https://doi.org/10.1061/(ASCE)0733-947X(1994)120:6(967)
Zeghal, M. & W. Khogali (2005). Predicting the resilient modulus of unbound granular materials by neural networks. In
I. Horvli (Ed.), Proceedings of the 7th BCRRA – International Conference on the Bearing Capacity of Roads, Railways and Airfields. URL: https://www.ntnu.no/ojs/index.php/BCRRA/article/view/3166 [visited 18/6/2026].
Zhang, H. & T. Yu (2016). Prediction of subgrade elastic moduli in different seasons based on backpropagation neural network technology. Road Materials and Pavement Design 19(2), 1–18. DOI:10.1080/14680629.2016.1259122. DOI: https://doi.org/10.1080/14680629.2016.1259122
Zumrawi, M. (2012). Prediction of CBR from index properties of cohesive soils. In Annual Conference of Postgraduate Studies and Scientific Research (Basic and Engineering Studies Board), Khartoum: Friendship Hall, pp. 1–9. DOI: https://doi.org/10.1201/b13165-118
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Antonio Júnior Alves Ribeiro, Carlos Augusto Uchôa da Silva , Suelly Helena de Araújo Barroso , João Paulo Ferreira de Lacerda, Pedro Mateus Santos Oliveira
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who submit papers for publication by TRANSPORTES agree to the following terms:
- The authors retain the copyright and grant Transportes the right of first publication of the manuscript, without any financial charge, and waive any other remuneration for its publication by ANPET.
- Upon publication by Transportes, the manuscript is automatically licensed under the Creative Commons License CC BY 4.0 license. This license permits the work to be shared with proper attribution to the authors and its original publication in this journal.
- Authors are authorized to enter into additional separate contracts for the non-exclusive distribution of the version of the manuscript published in this journal (e.g., publishing in an institutional repository or as a book chapter), with recognition of the initial publication in this journal, provided that such a contract does not imply an endorsement of the content of the manuscript or the new medium by ANPET.
- Authors are permitted and encouraged to publish and distribute their work online (e.g., in institutional repositories or on their personal websites) after the editorial process is complete. As Transportes provides open access to all published issues, authors are encouraged to use links to the DOI of their article in these cases.
- Authors confirm they have obtained all required employer permissions for the publication and CC BY 4.0 licensing of the manuscript, particularly if the employer holds any claim to the manuscript's copyright. Authors assume all responsibility for employer-related copyright issues, releasing ANPET and Transportes from any related liability.
- Authors assume full responsibility for the content of the manuscript, including the necessary and appropriate authorizations for the disclosure of collected data and obtained results, releasing ANPET and Transportes from any responsibility in this regard.
Last update: 11/27/2025
